<!doctype html>
<html lang="en-US">
<head>
  <meta http-equiv="Content-Type" content="text/html;charset=utf-8">
  <title>libMesh - A C++ Finite Element Library</title>
  <meta name="author" content="libMesh development team">
  <link rel="stylesheet" type="text/css" media="all" href="../styles.css">
  <link rel="stylesheet" type="text/css" media="all" href="../doxygen_stylesheet.css">
</head>

<body>
  <nav id="fixedbar">
    <ul id="fixednav">
      <li><a href="../index.html">Home</a></li>
      <li><a href="../support.html">About Us</a></li>
      <li><a href="../publications.html">Publications</a></li>
      <li><a href="https://github.com/libMesh/libmesh/graphs/contributors">Developers</a></li>
      <li><a href="../installation.html">Installation</a></li>
      <li><a href="../examples.html">Examples</a></li>
     <li><a href="https://mooseframework.inl.gov/docs/doxygen/libmesh/index.html">Documentation</a></li>
    </ul>
  </nav>

  <div id="w">
    <header id="logo"><a href="../index.html"><span id="logobg">SomeWebsiteLogo</span></a></header>

    <nav id="navigation">
      <ul>
        <li><a href="../index.html">Home</a></li>
        <li><a href="../support.html">About Us</a></li>
        <li><a href="../publications.html">Publications</a></li>
        <li><a href="https://github.com/libMesh/libmesh/graphs/contributors">Developers</a></li>
        <li><a href="../installation.html">Installation</a></li>
        <li><a href="../examples.html">Examples</a></li>
        <li><a href="https://mooseframework.inl.gov/docs/doxygen/libmesh/index.html">Documentation</a></li>
      </ul>
    </nav>

<div id="content">

<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/systems_of_equations/systems_of_equations_ex2" target="_blank">Open systems_of_equations_ex2 in new tab.</a>
<a name="output"></a> 
<br><br><br> <h1> The console output of the program: </h1> 
<pre>
***************************************************************
* Running Example systems_of_equations_ex2:
*   example-opt  
***************************************************************
 
 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=1681
    n_local_nodes()=1681
  n_elem()=400
    n_local_elem()=400
    n_active_elem()=400
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0

 EquationSystems
  n_systems()=1
   System #0, "Navier-Stokes"
    Type "TransientLinearImplicit"
    Variables={ "u" "v" } "p" 
    Finite Element Types="LAGRANGE", "JACOBI_20_00" "LAGRANGE", "JACOBI_20_00" 
    Infinite Element Mapping="CARTESIAN" "CARTESIAN" 
    Approximation Orders="SECOND", "THIRD" "FIRST", "THIRD" 
    n_dofs()=3803
    n_local_dofs()=3803
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    n_vectors()=3
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 38.9716
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 59
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0



*** Solving time step 0, time = 0.01 ***
Linear solver converged at step: 236, final residual: 0.000214866  Nonlinear convergence: ||u - u_old|| = 282.453
Linear solver converged at step: 90, final residual: 9.23274e-06  Nonlinear convergence: ||u - u_old|| = 0.743958
Linear solver converged at step: 250, final residual: 8.01557e-07  Nonlinear convergence: ||u - u_old|| = 0.0129303
Linear solver converged at step: 250, final residual: 1.29901e-09  Nonlinear convergence: ||u - u_old|| = 0.00156519
Linear solver converged at step: 250, final residual: 1.81135e-11  Nonlinear convergence: ||u - u_old|| = 1.9347e-06
 Nonlinear solver converged at step 4


*** Solving time step 1, time = 0.02 ***
Linear solver converged at step: 235, final residual: 0.000218713  Nonlinear convergence: ||u - u_old|| = 30.6378
Linear solver converged at step: 178, final residual: 1.06626e-05  Nonlinear convergence: ||u - u_old|| = 0.372807
Linear solver converged at step: 250, final residual: 5.32852e-08  Nonlinear convergence: ||u - u_old|| = 0.00603164
Linear solver converged at step: 250, final residual: 2.90971e-11  Nonlinear convergence: ||u - u_old|| = 0.000105181
 Nonlinear solver converged at step 3


*** Solving time step 2, time = 0.03 ***
Linear solver converged at step: 76, final residual: 0.00022519  Nonlinear convergence: ||u - u_old|| = 6.00785
Linear solver converged at step: 120, final residual: 1.02696e-05  Nonlinear convergence: ||u - u_old|| = 0.251248
Linear solver converged at step: 250, final residual: 8.05847e-07  Nonlinear convergence: ||u - u_old|| = 0.0163508
Linear solver converged at step: 250, final residual: 1.04342e-09  Nonlinear convergence: ||u - u_old|| = 0.00110321
Linear solver converged at step: 250, final residual: 1.07596e-10  Nonlinear convergence: ||u - u_old|| = 1.43612e-06
 Nonlinear solver converged at step 4


*** Solving time step 3, time = 0.04 ***
Linear solver converged at step: 72, final residual: 0.000219168  Nonlinear convergence: ||u - u_old|| = 2.18001
Linear solver converged at step: 107, final residual: 1.06522e-05  Nonlinear convergence: ||u - u_old|| = 0.26029
Linear solver converged at step: 250, final residual: 6.45964e-07  Nonlinear convergence: ||u - u_old|| = 0.0170193
Linear solver converged at step: 250, final residual: 3.95146e-09  Nonlinear convergence: ||u - u_old|| = 0.00105789
Linear solver converged at step: 250, final residual: 1.25745e-12  Nonlinear convergence: ||u - u_old|| = 4.47682e-06
 Nonlinear solver converged at step 4


*** Solving time step 4, time = 0.05 ***
Linear solver converged at step: 57, final residual: 0.00022426  Nonlinear convergence: ||u - u_old|| = 0.988783
Linear solver converged at step: 168, final residual: 1.09441e-05  Nonlinear convergence: ||u - u_old|| = 0.16081
Linear solver converged at step: 250, final residual: 9.82019e-07  Nonlinear convergence: ||u - u_old|| = 0.0129089
Linear solver converged at step: 250, final residual: 3.29125e-10  Nonlinear convergence: ||u - u_old|| = 0.00147557
Linear solver converged at step: 250, final residual: 1.37699e-11  Nonlinear convergence: ||u - u_old|| = 6.01585e-07
 Nonlinear solver converged at step 4


*** Solving time step 5, time = 0.06 ***
Linear solver converged at step: 52, final residual: 0.000214357  Nonlinear convergence: ||u - u_old|| = 0.476249
Linear solver converged at step: 172, final residual: 9.66487e-06  Nonlinear convergence: ||u - u_old|| = 0.203206
Linear solver converged at step: 250, final residual: 3.16979e-08  Nonlinear convergence: ||u - u_old|| = 0.0169568
Linear solver converged at step: 250, final residual: 1.94227e-09  Nonlinear convergence: ||u - u_old|| = 5.01869e-05
 Nonlinear solver converged at step 3


*** Solving time step 6, time = 0.07 ***
Linear solver converged at step: 22, final residual: 0.000212706  Nonlinear convergence: ||u - u_old|| = 0.256589
Linear solver converged at step: 127, final residual: 9.96381e-06  Nonlinear convergence: ||u - u_old|| = 0.152875
Linear solver converged at step: 250, final residual: 9.83166e-08  Nonlinear convergence: ||u - u_old|| = 0.00946214
Linear solver converged at step: 250, final residual: 8.34252e-10  Nonlinear convergence: ||u - u_old|| = 0.000133858
 Nonlinear solver converged at step 3


*** Solving time step 7, time = 0.08 ***
Linear solver converged at step: 19, final residual: 0.00019437  Nonlinear convergence: ||u - u_old|| = 0.152024
Linear solver converged at step: 59, final residual: 6.54079e-06  Nonlinear convergence: ||u - u_old|| = 0.0858625
Linear solver converged at step: 227, final residual: 6.54855e-09  Nonlinear convergence: ||u - u_old|| = 0.00281105
Linear solver converged at step: 239, final residual: 8.61149e-15  Nonlinear convergence: ||u - u_old|| = 3.58207e-07
 Nonlinear solver converged at step 3


*** Solving time step 8, time = 0.09 ***
Linear solver converged at step: 15, final residual: 0.000203605  Nonlinear convergence: ||u - u_old|| = 0.0866795
Linear solver converged at step: 119, final residual: 8.87784e-06  Nonlinear convergence: ||u - u_old|| = 0.0418116
Linear solver converged at step: 236, final residual: 1.77583e-08  Nonlinear convergence: ||u - u_old|| = 0.0068032
Linear solver converged at step: 250, final residual: 7.6203e-11  Nonlinear convergence: ||u - u_old|| = 2.37763e-05
 Nonlinear solver converged at step 3


*** Solving time step 9, time = 0.1 ***
Linear solver converged at step: 11, final residual: 0.000219903  Nonlinear convergence: ||u - u_old|| = 0.0505947
Linear solver converged at step: 70, final residual: 1.08505e-05  Nonlinear convergence: ||u - u_old|| = 0.0181966
Linear solver converged at step: 250, final residual: 4.55109e-08  Nonlinear convergence: ||u - u_old|| = 0.0127983
Linear solver converged at step: 250, final residual: 8.00529e-11  Nonlinear convergence: ||u - u_old|| = 7.19859e-05
 Nonlinear solver converged at step 3


*** Solving time step 10, time = 0.11 ***
Linear solver converged at step: 11, final residual: 0.000139303  Nonlinear convergence: ||u - u_old|| = 0.0322426
Linear solver converged at step: 105, final residual: 4.32521e-06  Nonlinear convergence: ||u - u_old|| = 0.012634
Linear solver converged at step: 229, final residual: 4.15933e-09  Nonlinear convergence: ||u - u_old|| = 0.00578586
Linear solver converged at step: 250, final residual: 4.24343e-11  Nonlinear convergence: ||u - u_old|| = 7.01804e-06
 Nonlinear solver converged at step 3


*** Solving time step 11, time = 0.12 ***
Linear solver converged at step: 10, final residual: 0.000145762  Nonlinear convergence: ||u - u_old|| = 0.020515
Linear solver converged at step: 48, final residual: 4.72567e-06  Nonlinear convergence: ||u - u_old|| = 0.00781656
Linear solver converged at step: 250, final residual: 3.20806e-08  Nonlinear convergence: ||u - u_old|| = 0.00687872
Linear solver converged at step: 250, final residual: 1.55861e-10  Nonlinear convergence: ||u - u_old|| = 4.04035e-05
 Nonlinear solver converged at step 3


*** Solving time step 12, time = 0.13 ***
Linear solver converged at step: 10, final residual: 9.33348e-05  Nonlinear convergence: ||u - u_old|| = 0.0136033
Linear solver converged at step: 67, final residual: 1.95952e-06  Nonlinear convergence: ||u - u_old|| = 0.00578775
Linear solver converged at step: 250, final residual: 2.69457e-08  Nonlinear convergence: ||u - u_old|| = 0.00252266
Linear solver converged at step: 250, final residual: 2.49022e-10  Nonlinear convergence: ||u - u_old|| = 4.23675e-05
 Nonlinear solver converged at step 3


*** Solving time step 13, time = 0.14 ***
Linear solver converged at step: 9, final residual: 0.00015015  Nonlinear convergence: ||u - u_old|| = 0.00909494
Linear solver converged at step: 19, final residual: 3.93378e-06  Nonlinear convergence: ||u - u_old|| = 0.00478245
Linear solver converged at step: 250, final residual: 7.99254e-09  Nonlinear convergence: ||u - u_old|| = 0.00217195
Linear solver converged at step: 250, final residual: 1.58995e-09  Nonlinear convergence: ||u - u_old|| = 9.28168e-06
 Nonlinear solver converged at step 3


*** Solving time step 14, time = 0.15 ***
Linear solver converged at step: 8, final residual: 0.000160079  Nonlinear convergence: ||u - u_old|| = 0.00592993
Linear solver converged at step: 17, final residual: 5.46766e-06  Nonlinear convergence: ||u - u_old|| = 0.0036996
Linear solver converged at step: 250, final residual: 1.09116e-08  Nonlinear convergence: ||u - u_old|| = 0.00118612
Linear solver converged at step: 250, final residual: 2.13422e-11  Nonlinear convergence: ||u - u_old|| = 1.57131e-05
 Nonlinear solver converged at step 3

 -------------------------------------------------------------------------------------------------------------------
| Time:           Wed Apr 13 09:57:30 2016                                                                          |
| OS:             Darwin                                                                                            |
| HostName:       peterson-laptop.local                                                                             |
| OS Release:     15.0.0                                                                                            |
| OS Version:     Darwin Kernel Version 15.0.0: Sat Sep 19 15:53:46 PDT 2015; root:xnu-3247.10.11~1/RELEASE_X86_64  |
| Machine:        x86_64                                                                                            |
| Username:       petejw                                                                                            |
| Configuration:  ../configure  'INSTALL=/usr/bin/install -C'                                                       |
|  '--with-methods=opt dbg'                                                                                         |
|  '--prefix=/Users/petejw/projects/libmesh_git/installed'                                                          |
|  '--enable-perflog'                                                                                               |
|  '--enable-tracefiles'                                                                                            |
|  '--disable-blocked-storage'                                                                                      |
|  '--enable-default-comm-world'                                                                                    |
|  '--enable-tecio'                                                                                                 |
|  '--enable-unique-ptr'                                                                                            |
|  '--enable-ifem'                                                                                                  |
|  'PETSC_DIR=/opt/moose/petsc/mpich_petsc-3.6.1/clang-opt-superlu'                                                 |
|  'SLEPC_DIR=/opt/petejw/slepc/3.6.1'                                                                              |
|  'CPPFLAGS= '                                                                                                     |
|  'LIBS= '                                                                                                         |
|  'CPPFLAGS=  '                                                                                                    |
|  'LIBS=  '                                                                                                        |
|  '--disable-netcdf-4'                                                                                             |
|  '--disable-testsets'                                                                                             |
|  'CXX=mpicxx'                                                                                                     |
|  'CC=mpicc'                                                                                                       |
|  'F77=mpif77'                                                                                                     |
|  'FC=mpif90'                                                                                                      |
|  'CPPFLAGS=   '                                                                                                   |
|  'LIBS=   '                                                                                                       |
 -------------------------------------------------------------------------------------------------------------------
 ------------------------------------------------------------------------------------------------------------
| Systems Example 2 Performance: Alive time=3.82638, Active time=3.77428                                     |
 ------------------------------------------------------------------------------------------------------------
| Event                         nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                          w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|------------------------------------------------------------------------------------------------------------|
|                                                                                                            |
| linear solve                  64         3.7743      0.058973    3.7743      0.058973    100.00   100.00   |
 ------------------------------------------------------------------------------------------------------------
| Totals:                       64         3.7743                                          100.00            |
 ------------------------------------------------------------------------------------------------------------

 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=4.19057, Active time=3.80747                                                    |
 -----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     1          0.0003      0.000261    0.0003      0.000261    0.01     0.01     |
|   build_sparsity()                 1          0.0036      0.003647    0.0039      0.003943    0.10     0.10     |
|   create_dof_constraints()         1          0.0001      0.000078    0.0001      0.000078    0.00     0.00     |
|   distribute_dofs()                1          0.0004      0.000372    0.0016      0.001622    0.01     0.04     |
|   dof_indices()                    120800     0.0350      0.000000    0.0350      0.000000    0.92     0.92     |
|   prepare_send_list()              2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         1          0.0013      0.001250    0.0013      0.001250    0.03     0.03     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_solution_vector()          15         0.0145      0.000963    0.0200      0.001335    0.38     0.53     |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               15         0.0242      0.001611    0.0242      0.001611    0.63     0.63     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        51200      0.0739      0.000001    0.0739      0.000001    1.94     1.94     |
|   init_shape_functions()           128        0.0006      0.000004    0.0006      0.000004    0.01     0.01     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_affine_map()             51200      0.0387      0.000001    0.0387      0.000001    1.02     1.02     |
|   init_reference_to_physical_map() 128        0.0012      0.000010    0.0012      0.000010    0.03     0.03     |
|                                                                                                                 |
| Mesh                                                                                                            |
|   all_second_order()               1          0.0016      0.001593    0.0016      0.001593    0.04     0.04     |
|   find_neighbors()                 2          0.0022      0.001080    0.0022      0.001080    0.06     0.06     |
|   renumber_nodes_and_elem()        4          0.0001      0.000017    0.0001      0.000017    0.00     0.00     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         15         0.0002      0.000011    0.0444      0.002957    0.00     1.17     |
|                                                                                                                 |
| MeshTools::Generation                                                                                           |
|   build_cube()                     1          0.0012      0.001223    0.0012      0.001223    0.03     0.03     |
|                                                                                                                 |
| Parallel                                                                                                        |
|   allgather()                      1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   single_partition()               2          0.0001      0.000034    0.0001      0.000034    0.00     0.00     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          64         2.9896      0.046713    2.9896      0.046713    78.52    78.52    |
|                                                                                                                 |
| System                                                                                                          |
|   assemble()                       64         0.6190      0.009672    0.7807      0.012199    16.26    20.50    |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            223647     3.8075                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------

 
***************************************************************
* Done Running Example systems_of_equations_ex2:
*   example-opt  
***************************************************************
</pre>
</div>

<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script type="text/javascript">
$(document).ready(function(){
  $(window).on('scroll',function() {
    var scrolltop = $(this).scrollTop();

    if(scrolltop >= 215) {
      $('#fixedbar').fadeIn(250);
    }

    else if(scrolltop <= 210) {
      $('#fixedbar').fadeOut(250);
    }
  });
});
</script>

<!-- Google Analytics stuff -->
<script type="text/javascript">
  var _gaq = _gaq || [];
  _gaq.push(['_setAccount', 'UA-24978333-1']);
  _gaq.push(['_trackPageview']);
  (function() {
    var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
    ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
    var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
  })();
</script>

</body>
</html>
